Why musicians make good programmers

I was chatting to someone the other day and we got talking about the other things we did besides programming.  It turns out that both of us were musicians.  I got to thinking and realized that I knew at least six technical people who were also musicians -- and pretty good ones, at that.

It's an old maxim that musicians are likely to make good programmers, but most of the time the reasons why it might be true are left unsaid.  I've received the impression that the association is something like music --> rhythm --> counting --> math --> programming.

Personally, I think the reasons are quite other.  As someone who's spent a long time doing both, I think that what programming and instrumental music performance study have in common is a certain set of mental skills.  In both cases, you have to take something that's quite abstract (and perhaps only vaguely conceived), flesh out its shape in your mind, take it apart, put it back together, and then translate it into something concrete:  property definitions, muscle movements, rises and falls in volume.  There's a degree of analytical skill, pattern-matching, and pattern-mapping that's required in both.